4 papers
The Minkowski equality and inequality for multiplicity of ideals
Kriti Goel, R. V. Gurjar, J. K. Verma
In this exposition of the equality and inequality of Minkowski for multiplicity of ideals, we provide simple algebraic and geometric proofs. Connections with mixed multiplicities o…
Eakin-Sathaye type theorems for joint reductions and good filtrations of ideals
Kriti Goel, Sudeshna Roy, J. K. Verma
Analogues of Eakin-Sathaye theorem for reductions of ideals are proved for -graded good filtrations. These analogues yield bounds on joint reduction vectors for a fa…
Variations on the Grothendieck-Serre Formula for Hilbert functions and their applications
Shreedevi K. Masuti, Parangama Sarkar, J. K. Verma
In this expository paper we present proofs of Grothendieck-Serre Formula for multi-graded algebras and Rees algebras for admissible multi-graded filtrations. As applications, we de…
Grothendieck-Serre formula and bigraded Cohen-Macaulay Rees algebras
A. V. Jayanthan, J. K. Verma
The Grothendieck-Serre formula for the difference between the Hilbert function and Hilbert polynomial of a graded algebra is generalized for bigraded standard algebras. This is use…